Find each of the following for the given f(x) & g(x)

Question

a. (fg)(2) b. (f-g)(x) c. (fog)(x) f(x)=1/x , g(x)=2/x? 

 

 

Answer 1

The functions are f(x) = 1/x and g(x) = 2/x

a. (fg)(2)

(fg)(x) = f(x) g(x)

         = (1/x) (2/x)

         = 2/x²

(fg)(x) =  2/x²

(fg)(2) = 2/(2)²

          = 1/2

(fg)(2) = 1/2.

b.(f - g)(x) = f(x) - g(x)

               = (1/x) - (2/x)

               = - 1/x

(f - g)(x) = - 1/x.

c.(fog)(x) = f(g(x))

Substitute the expression for functioning g (in this case 2/x) for g(x) in the composition.

= f(2/x)

Now substitute this expression (1/x) in to function f in place of the x value.

= 1/(2/x)

= x/2

(fog)(x) = x/2.